! Copyright (c) 2007, 2008 Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: grouping kernel make math.order sequences project-euler.common ;
IN: project-euler.011

! http://projecteuler.net/index.php?section=problems&id=11

! DESCRIPTION
! -----------

! In the 20x20 grid below, four numbers along a diagonal line have been marked
! in red.

!     08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
!     49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
!     81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
!     52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
!     22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
!     24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
!     32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
!     67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
!     24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
!     21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
!     78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
!     16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
!     86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
!     19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
!     04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
!     88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
!     04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
!     20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
!     20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
!     01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

! The product of these numbers is 26 * 63 * 78 * 14 = 1788696.

! What is the greatest product of four numbers in any direction (up, down,
! left, right, or diagonally) in the 20x20 grid?


! SOLUTION
! --------

<PRIVATE

: horizontal ( -- matrix )
    {
      08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
      49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
      81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
      52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
      22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
      24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
      32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
      67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
      24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
      21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
      78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
      16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
      86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
      19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
      04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
      88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
      04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
      20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
      20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
      01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48
    } 20 group ;

: vertical ( -- matrix )
    horizontal flip ;

: pad-front ( matrix -- matrix )
    [
        length <iota> [ 0 <repetition> ] map
    ] keep [ append ] 2map ;

: pad-back ( matrix -- matrix )
    <reversed> [
        length <iota> [ 0 <repetition> ] map
    ] keep [ <reversed> append ] 2map ;

: diagonal/ ( -- matrix )
    horizontal reverse pad-front pad-back flip ;

: diagonal\ ( -- matrix )
    horizontal pad-front pad-back flip ;

: max-product ( matrix width -- n )
    [ clump ] curry map concat
    [ product ] [ max ] map-reduce ; inline

PRIVATE>

: euler011 ( -- answer )
    [
        { [ horizontal ] [ vertical ] [ diagonal/ ] [ diagonal\ ] }
        [ call( -- matrix ) 4 max-product , ] each
    ] { } make supremum ;

! [ euler011 ] 100 ave-time
! 3 ms ave run time - 0.77 SD (100 trials)

SOLUTION: euler011
